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Advanced Problems in Mathematics: Preparing for University

This book is intended to help students prepare for entrance examinations in mathematics and scientific subjects, including STEP (Sixth Term Examination Papers). STEP examinations are used by Cambridge colleges as the basis for conditional offers in mathematics and sometimes in other mathematics-related subjects. They are also used by Warwick University, and many other mathematics departments recommend that their applicants practice on past papers to become accustomed to university-style mathematics.

Advanced Problems in Mathematics is recommended as preparation for any undergraduate mathematics course, even for students who do not plan to take the Sixth Term Examination Paper. The questions analysed in this book are all based on recent STEP questions selected to address the syllabus for Papers I and II, which is the A-level core (i.e. C1 to C4) with a few additions. Each question is followed by a comment and a full solution. The comments direct the reader’s attention to key points and put the question in its true mathematical context. The solutions point students to the methodology required to address advanced mathematical problems critically and independently.

This book is a must read for any student wishing to apply to scientific subjects at university level and for anybody interested in advanced mathematics.

Please note that in this book the mathematical formulas are encoded in MathML. While reading the HTML version, you can right-click on any of the formulas to display the underlying code.

The DfE (Department for Education) has generously contributed towards the publication of this volume.

Stephen Siklos lectures in the Faculty of Mathematics at Cambridge University. His main area of research is Einstein's theory of General Relativity. For many years, Dr Siklos was the Admissions Officer for the Faculty of Mathematics, dealing with issues at the interface of school and university mathematics. He has presided over the STEP examinations, used as a qualification for undergraduate admissions by some of the top British university mathematics departments, for thirty years. Dr Siklos lives in Cambridge with his partner, who is a geologist, and their two children. He very much likes playing tennis, listening to music and reading old examination papers.

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